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On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation
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On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation

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Abstract:

In the framework of the special theory of relativity, elementary formulas are used to derive the formula for determining the relativistic angular momentum of a rotating ideal uniform ball. The moment of inertia of such a ball turns out to be a nonlinear function of the angular velocity of rotation. Application of this formula to the neutron star PSR J1614-2230 shows that due to relativistic corrections the angular momentum of the star increases tenfold as compared to the nonrelativistic formula. For the proton and neutron star PSR J1748-2446ad the velocities of their surface’s motion are calculated, which reach the values of the order of 30% and 19% of the speed of light, respectively. Using the formula for the relativistic angular momentum of a uniform ball, it is easy to obtain the formula for the angular momentum of a thin spherical shell depending on its thickness, radius, mass density, and angular velocity of rotation. As a result, considering a spherical body consisting of a set of such shells it becomes possible to accurately determine its angular momentum as the sum of the angular momenta of all the body’s shells. Two expressions are provided for the maximum possible angular momentum of the ball based on the rotation of the ball’s surface at the speed of light and based on the condition of integrity of the gravitationally bound body at the balance of the gravitational and centripetal forces. Comparison with the results of the general theory of relativity shows the difference in angular momentum of the order of 25% for an extremal Kerr black hole.

Info:

Periodical:
International Frontier Science Letters (Volume 15)
Pages:
9-14
DOI:
https://doi.org/10.18052/www.scipress.com/IFSL.15.9
Citation:
S. G. Fedosin, "On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation", International Frontier Science Letters, Vol. 15, pp. 9-14, 2020
Online since:
February 2020
Authors:
Sergey G. Fedosin
Keywords:
Moment of Inertia, Neutron Star, Relativistic Angular Momentum
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Distribution:
Open Access

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References:

[1] Molina A. and Ruiz E. An approximate global solution of Einstein's equations for a differentially rotating compact body. General Relativity and Gravitation, Vol. 49, no 10, p.135 (2017).

DOI: https://doi.org/10.1007/s10714-017-2297-5

[2] Demorest P. B., Pennucci T., Ransom S.M., Roberts M.S.E., Hessels J.W.T. A two-solar-mass neutron star measured using Shapiro delay. Nature. Vol. 467 (7319), pp.1081-1083 (2010).

DOI: https://doi.org/10.1038/nature09466

[3] Fedosin S.G. Estimation of the physical parameters of planets and stars in the gravitational equilibrium model. Canadian Journal of Physics, Vol. 94, no. 4, pp.370-379 (2016).

DOI: https://doi.org/10.1139/cjp-2015-0593

[4] Fedosin S.G. The radius of the proton in the self-consistent model. Hadronic Journal, Vol. 35, no. 4, pp.349-363 (2012).

[5] Hessels J.W.T., Ransom S.M., Stairs I.H., Freire P.C.C., Kaspi V.M., Camilo F. A Radio Pulsar Spinning at 716 Hz. Science. Vol. 311 (5769), pp.1901-1904 (2006).

DOI: https://doi.org/10.1126/science.1123430
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